Baccarat is one of the many live table games played in casinos or gaming establishments. Baccarat uses a standard deck of 52 playing cards and is usually dealt from a shoe having multiple decks that have been shuffled together prior to the beginning of play.
The object of the game of Baccarat is for the bettor to successfully wager on whether the Bank's hand or the Player's hand is going to win. The bettor receives even money for his wager if he selects the winning hand and loses his wager if he selects the losing hand. Because of the rules of play of Baccarat and more particularly the pre-established draw rules, the Bank's hand has a slightly higher chance of winning than does the Player's hand. The winning frequency for the Bank's hand has been determined to be 0.45859 (45.859%) whereas the winning frequency for the Player hand is 0.44624 (44.624%) with the remainder of the outcomes being ties. Therefore, if the bettor wagers on the Bank's hand and the Bank hand wins, the bettor must pay to the gaming establishment a commission (typically, 5%) of the amount the bettor wins. No commission is paid if the bettor successfully wagers on the Player's hand.
As used in this specification, the term "Conventional Manner of Play of Baccarat" is as follows:
A multiple number of decks of standard playing cards, 52 in number, are used; typically eight decks are shuffled together and placed in a shoe from which the cards are dealt during the play of the game.
Each bettor makes a wager on whether the Bank's hand or the Player's hand will win. After all wagers are made, two cards are dealt from the shoe to the Bank position and two cards are dealt from the shoe to the Player position on the table layout. The cards are turned face up and the value of the Bank hand the Player hand is determined, modulo ten.
Aces count one; Kings, Queens, Jacks and Tens count zero and the other cards count their respective face value. The suits (Spades, Hearts, Diamonds and Clubs) have no meaning in Baccarat.
The highest hand value in Baccarat is nine. All hand values range from a low of zero to a high of nine. If when the cards are added together, the total of the hand exceeds nine, then the hand value is determined modulo ten. For example, a seven and a eight total fifteen, but the hand value is five. An Ace and a nine total ten, but the hand value is zero.
A two card total of eight or nine is called a "natural"; a two card total of zero is called a "baccarat." As will be explained below, in certain situations in the play of the game, a third card will be dealt. The value of this third card is added to the total of the first two cards and a new hand value is established. Again, if the new hand total exceeds nine, the hand value is determined by subtracting ten from the total of the hand.
Prior to the deal, each better can make one of three wagers: 1) that the Bank hand will win; 2) that the Player hand will win; or 3) that the Bank hand and the Player hand will tie. Wagering locations are provided on the Baccarat table layout. Whichever of the Bank hand or the Player hand is closest to a total on nine is the winner.
All winning Bank hand wagers are paid off at odds of one-to-one and the house charges a five percent (5%) commission on the amount won by the bettor. For example, if a bettor wagers $100 on the Bank hand and the Bank hand wins, the bettor wins $100 and is charged a $5 commission on the amount that the bettor won. The bettor is not charged any commission on the amount of his wager.
All winning Player hand wagers are paid off at odds of one-to-one and the bettor is not charged any commission on the amount of his winnings or his wager because the house, by virtue of the third card draw rules, has a statistical advantage over the player of 45.859-44.624 or 1.235% which is the vigorish ("vig") of the house on player wagers. Winning wagers on the Tie hand bet are paid off at odds of nine-to-one or eight-to-one (depending on the gaming establishment) and the bettor is not charged any commission on the amount of his winnings or his wager since there is already a statistical advantage in favor of the house on tie wagers. If a Tie hand occurs, all wagers on the Bank hand and all wagers on the Player hand are "pushes" and the amount wagered is returned to the bettor.
Depending on the point total of the Player's hand and the Dealer's hand, one more card may be dealt to either the Player's hand, the Dealer's hand or both. The rules for determining whether a third card is dealt are fixed rules, there is no discretion for either the Player's hand or the Dealer's hand on whether a third card is dealt.
If either the Player hand or the Dealer hand has a point total of eight or nine on the first two cards, no third card is dealt to either hand and the hand with the highest point total is the winner (or the hand is a Tie, as the case may be). If neither the Player hand or the Dealer hand has a point total of eight or nine, then there is a possibility of a third card draw.
The third card draw rules are as follows:
Rule #1: If the initial two card Player hand has a point total of 0, 1, 2, 3, 4 or 5, the Player hand draws a third card. If the initial two card Player hand has a point total of 6 or 7, the Player hand stands and does not receive a third card.
Rule 12: If the Player hand stands and does not draw a third card, then the Bank hand follows Rule #1. In other words, if the Player hand has a point total of 6 or 7, the Bank hand draws a third card on a point total of 0, 1, 2, 3, 4 or 5 and the Bank hand stands on a point total of 6 or 7.
Rule 13: If the Player hand draws a third card, the Bank hand must draw or stand as follows:
______________________________________ Bank hand Bank hand DRAWS Bank hand STANDS two card when the Player's when the Player's point total hand third card is: hand third card is: ______________________________________ 0, 1 or 2 Bank always draws 3 0, 1, 2, 3, 4, 5, 6, 7 or 9 8 4 2, 3, 4, 5, 6 or 7 0, 1, 8 or 9 5 4, 5, 6 or 7 0, 1, 2, 3, 8 or 9 6 6 or 7 0, 1, 2, 3, 4, 5, 8 or 9 7 Bank always stands ______________________________________
The draw rules for Conventional baccarat are shown in Table 1 below.
TABLE 1 __________________________________________________________________________ BACCARAT RULES __________________________________________________________________________ PLAYER HAVING TWO CARD TOTAL OF __________________________________________________________________________ 1-2-3-4-5-10 DRAWS A CARD 6-7 STANDS 8-9 TURNS CARDS OVER __________________________________________________________________________ BANKER DOES NOT DRAW HAVING DRAWS WHEN GIVING WHEN GIVING TWO CARD OR PLAYER'S THIRD CARD DRAW IS OR PLAYER'S THIRD CARD TOTAL OF AN DRAW IS AN __________________________________________________________________________ 0, 1, 2 ALWAYS DRAWS 3 1-2-3-4-5-6-7-9-10 8 4 2-3-4-5-6-7 1-8-9-10 5 4-5-6-7 1-2-3-8-9-10 6 6-7 1-2-3-4-5-8-9-10 7 STANDS 8-9 TURNS CARDS OVER __________________________________________________________________________
At the end of each hand, winning wagers are paid and losing wagers are collected by the house. Any commission due to the house is marked in commission boxes in the center of the table. Gaming chips are used to represent the amount of money owed by each bettor to the house for the commissions. In order not to slow down the game, the commission is not actually collected from each bettor until the end of the round determined by all of the cards in the shoe being dealt down to the plastic cut card, usually approximately eighty hands.
The mathematical analysis of the game reveals that the 5% commission is what gives the house its advantage on wagers on the Banker hand and allows the gaming establishment to make a profit from providing the Baccarat game to the bettors. Because the rules for standing and drawing third cards are automatic, the mathematical analysis shows that the Bank hand will win 45.859% of the hands, the Player hand will win 44.624% of the hands and the Tie hand will occur 9.517% of the hands. If the Tie hands are disregarded because they do not affect any Player or Bank wagers, it is then determined that the Bank hand will win 50.7% of the time and the Player hand will win 49.3% of the time.
Because the Bank hand wins more than 50% of the hands (disregarding the Tie hands that do not affect any Player or Bank wagers), if a bettor always bet on the Bank hand, the bettor would have an advantage over the gaming establishment. By charging a 5% commission on all Bank hand wins, the gaming establishment compensates for the percentage of winning Bank hands being slightly over 50%.
After figuring in the 5% commission that must be paid by bettors on winning Bank hands, the gaming establishment has approximately a 1.23% advantage over the bettor when the bettor wagers on the Player hand and the gaming establishment has a 1.057% advantage over the bettor when the bettor wagers on the Bank hand. The Tie hand wager gives the gaming establishment a 4.88% advantage over the bettor when the payoff odds are nine-to-one and a 14.1% advantage over the bettor when the payoff odds are eight-to-one.
One of the detriments of the conventional manner of play of Baccarat is the necessity for calculating, recording and collecting this 5% commission on all winning Bank hand wagers. Many people are reluctant to sit down and participate because they do not understand why they should have to pay a 5% commission on winning Bank hand wagers. They may consider this unfair and something extra for the gaming establishment.
The gaming establishments also suffer disadvantages from the 5% commission. The determination of the 5% amount is done visually by a casino dealer and is subject to casino dealer error and disputes with the bettors over the amount of the commission. The reconciliation and collection of the commission at the end of each shoe can result in delays of the beginning of the next round of play. If a bettor loses all of his money ("taps out") during a round of the game, the gaming establishment may have difficulty collecting the unpaid commission that has accrued to that bettor during that round of the game. It has been estimated that as much as twenty percent of the accrued commission goes uncollected. Because the house margin on Baccarat is so small, uncollected commissions can seriously impact the profitability of a Baccarat table or the entire Baccarat pit, if more than one table is in play. In certain situations a bettor will negotiate with the casino for the casino to forgive or discount the owed commissions, the quid pro quo being that the player will likely return to the casino in the future
Another detriment of the conventional manner of play of Baccarat is the complexity of the "third card" draw rules. These complicated rules deter new bettors from participating in the play of Baccarat.
To overcome these drawbacks we devised a modified baccarat game as disclosed in U.S. Pat. No. 5,362,064 issued Nov. 8, 1994 the disclosure of which is hereby incorporated by reference. In this patent we disclosed designating certain Banker and Player hand outcomes as "bar" hands for players wager on the Banker. As but an example where the Bank hand has a two card total of 4 and the Player has a hand total of 0, 1 or 2, paying wagers on the Bank is barred. By barring certain payoffs the vig provided by the 5% commission is statistically incorporated into the game and therefore need not be separately collected.
Because any modified, no commission game must be acceptable to both the players and the house there are several competing considerations. One consideration is that the game should have at least close to the same house advantage as Conventional baccarat including the commission. If the game has a higher vig than Conventional baccarat, there is no incentive to players to play a modified game. If the vig is lower, casinos may be reluctant to provide the game unless they make a conscious decision to offer a better game to entice players.
A drawback of providing the modified game designating certain hands as pushes is that to provide a vig comparable to that of Conventional baccarat only certain outcomes can be used. Thus a casino elects to bar certain hands, the vig and the hand combinations are determined. There is only limited flexibility in selecting barring outcomes.
Further there is no suitable means to infinitely adjust the vigorish. When certain outcomes are selected as barred hands, the vigorish is determined and cannot be adjusted.
A further drawback is that the casino cannot adjust the game to make the bar situations less complex. It would be desirable to provide a modified baccarat game where the casino can select a desired vigorish and select one or more certain, and easy to understand, combinations to operate upon to obtain the desired objective.